"Published in Vacaville, California, USA"
Find dy/dx and d2y/dx2 by implicit differentiation for:
Solution:
Consider the given equation above
Take the first derivative of the given equation with respect to x by implicit differentiation, we have
Finally, take the second derivative of the above equation with respect to x by implicit differentiation, we have
but
Hence, the above equation becomes
We can further simplify the above equation by using the given equation as follows
Therefore,
